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diff --git a/Master/texmf-dist/doc/latex/mil3/multline.tpl b/Master/texmf-dist/doc/latex/mil3/multline.tpl new file mode 100644 index 00000000000..09ad30d23bc --- /dev/null +++ b/Master/texmf-dist/doc/latex/mil3/multline.tpl @@ -0,0 +1,495 @@ +% Sample file: multline.tpl +% multiline math formula template file + + +% Section 5.2 Gathering formulas + +\begin{gather} + x_{1} x_{2} + x_{1}^{2} x_{2}^{2} + x_{3}, \label{E:mm1.1}\\ + x_{1} x_{3} + x_{1}^{2} x_{3}^{2} + x_{2}, \label{E:mm1.2}\\ + x_{1} x_{2} x_{3}. \label{E:mm1.3} +\end{gather} + +% 5.3 Splitting a long formula + +\begin{multline}\label{E:mm2} + (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\ + + (y_{1} y_{2} y_{3} y_{4} y_{5} +y_{1} y_{3} y_{4} y_{5} y_{6} + + y_{1} y_{2} y_{4} y_{5} y_{6} + + y_{1} y_{2} y_{3} y_{5} y_{6})^{2}\\ + + (z_{1} z_{2} z_{3} z_{4} z_{5} +z_{1} z_{3} z_{4} z_{5} z_{6} + + z_{1} z_{2} z_{4} z_{5} z_{6} + + z_{1} z_{2} z_{3} z_{5} z_{6})^{2}\\ + + (u_{1} u_{2} u_{3} u_{4} + u_{1} u_{2} u_{3} u_{5} + + u_{1} u_{2} u_{4} u_{5} + u_{1} u_{3} u_{4} u_{5})^{2} +\end{multline} + +\begin{multline*} + (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\ + + (x_{1} x_{2} x_{3} x_{4} x_{5} + + x_{1} x_{3} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}\\ + + (x_{1} x_{2} x_{3} x_{4} + x_{1} x_{2} x_{3} x_{5} + + x_{1} x_{2} x_{4} x_{5} + x_{1} x_{3} x_{4} x_{5})^{2} +\end{multline*} +\begin{setlength}{\multlinegap}{0pt} + \begin{multline*} + (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\ + + (x_{1} x_{2} x_{3} x_{4} x_{5} + + x_{1} x_{3} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}\\ + + (x_{1} x_{2} x_{3} x_{4} + x_{1} x_{2} x_{3} x_{5} + + x_{1} x_{2} x_{4} x_{5} + x_{1} x_{3} x_{4} x_{5})^{2} + \end{multline*} +\end{setlength} + +\begin{multline*} + (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\ + \shoveleft{+ (x_{1} x_{2} x_{3} x_{4} x_{5} + + x_{1} x_{3} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}}\\ + + (x_{1} x_{2} x_{3} x_{4} + x_{1} x_{2} x_{3} x_{5} + + x_{1} x_{2} x_{4} x_{5} + x_{1} x_{3} x_{4} x_{5})^{2} +\end{multline*} + +% 5.4.3 Group numbering + +\begin{gather} + x_{1} x_{2} + x_{1}^{2} x_{2}^{2} + x_{3},\label{E:mm1} \\ + x_{1} x_{3} + x_{1}^{2} x_{3}^{2} + x_{2},\tag{\ref{E:mm1}a}\\ + x_{1} x_{2} x_{3};\tag{\ref{E:mm1}b} +\end{gather} + +\begin{subequations}\label{E:gp} + \begin{gather} + x_{1} x_{2} + x_{1}^{2} x_{2}^{2} + x_{3},\label{E:gp1}\\ + x_{1} x_{3} + x_{1}^{2} x_{3}^{2} + x_{2},\label{E:gp2}\\ + x_{1} x_{2} x_{3},\label{E:gp3} + \end{gather} +\end{subequations} + + % 5.5 Aligned columns + +\begin{align}\label{E:mm3} + f(x) &= x + yz & g(x) &= x + y + z\\ + h(x) &= xy + xz + yz & k(x) &= (x + y)(x + z)(y + z) + \notag +\end{align} + +% 5.5.1 An align variant + +\begin{flalign}\label{E:mm3fl} + f(x) &= x + yz & g(x) &= x + y + z\\ + h(x) &= xy + xz + yz & k(x) &= (x + y)(x + z)(y + z) + \notag +\end{flalign} + +% 5.5.2 eqnarray, the ancestor of align + +\begin{eqnarray} + x & = & 17y \\ + y & > & a + b + c +\end{eqnarray} + +\begin{align} + x & = 17y \\ + y & > a + b + c +\end{align} + +% 5.5.3 The subformula rule revisited + +\begin{align} + x_{1} + y_{1} + \left( \sum_{i < 5} \binom{5}{i} + &+ a^{2} \right)^{2}\\ + \left( \sum_{i < 5} \binom{5}{i} + \alpha^{2} \right)^{2} +\end{align} + +\begin{align*} + &x_{1} + y_{1} + \left( \sum_{i < 5} \binom{5}{i} + + a^{2} \right)^{2}\\ + &\phantom{x_{1} + y_{1} + {}} + \left( \sum_{i < 5} \binom{5}{i} + \alpha^{2} \right)^{2} +\end{align*} + +% 5.5.4 The alignat environment + +\begin{alignat}{2}\label{E:mm3A} + f(x) &= x + yz & g(x) &= x + y + z\\ + h(x) &= xy + xz + yz & k(x) &= (x + y)(x + z)(y + z) + \notag +\end{alignat} + +\begin{alignat}{2}\label{E:mm3B} + f(x) &= x + yz & g(x) &= x + y + z\\ + h(x) &= xy + xz + yz \qquad & k(x) &= (x + y)(x + z)(y + z) + \notag + +\begin{alignat}{2}\label{E:mm4} + x &= x \wedge (y \vee z) & &\quad\text{(by distributivity)}\\ + &= (x \wedge y) \vee (x \wedge z) & & + \quad\text{(by condition (M))}\notag\\ + &= y \vee z \notag +\end{alignat} + +\begin{alignat}{2} + (A + B C)x &+{} &C &y = 0,\\ + Ex &+{} &(F + G)&y = 23. +\end{alignat} + +\begin{alignat}{4} + a_{11}x_1 &+ a_{12}x_2 &&+ a_{13}x_3 && &&= y_1,\\ + a_{21}x_1 &+ a_{22}x_2 && &&+ a_{24}x_4 &&= y_2,\\ + a_{31}x_1 & &&+ a_{33}x_3 &&+ a_{34}x_4 &&= y_3. +\end{alignat} + +% 5.5.5 Intertext + +\begin{align}\label{E:mm5} + h(x) &= \int \left( + \frac{ f(x) + g(x) } + {1 + f^{2}(x)} + + \frac{1 + f(x)g(x)} + { \sqrt{1 - \sin x} } + \right) \, dx\\ + \intertext{The reader may find the following form easier to + read:} + &= \int \frac{1 + f(x)} + {1 + g(x)} + \, dx - 2 \arctan(x - 2) \notag +\end{align} + +\begin{align*} + f(x) &= x + yz & \qquad g(x) &= x + y + z \\ + \intertext{The reader also may find the following + polynomials useful:} + h(x) &= xy + xz + yz + & \qquad k(x) &= (x + y)(x + z)(y + z) +\end{align*} + +% 5.6 Aligned subsidiary math environments + +% 5.6.1 Subsidiary variants of aligned math environments + +\[ + \begin{aligned} + x &= 3 + \mathbf{p} + \alpha \\ + y &= 4 + \mathbf{q}\\ + z &= 5 + \mathbf{r} \\ + u &=6 + \mathbf{s} + \end{aligned} + \text{\qquad using\qquad} + \begin{gathered} + \mathbf{p} = 5 + a + \alpha \\ + \mathbf{q} = 12 \\ + \mathbf{r} = 13 \\ + \mathbf{s} = 11 + d + \end{gathered} +\] + +\begin{align}\label{E:mm5} + h(x) &= \int \left( + \frac{ f(x) + g(x) } + {1 + f^{2}(x)} + + \frac{1 + f(x)g(x)} + { \sqrt{1 - \sin x} } + \right) \, dx\\ + \intertext{The reader may find the following form easier to + read:} + &= \int \frac{1 + f(x)} + {1 + g(x)} + \, dx - 2 \arctan(x - 2) \notag +\end{align} + +\begin{equation}\label{E:mm6} + \begin{aligned} + h(x) &= \int \left( + \frac{ f(x) + g(x) } + { 1 + f^{2}(x) } + + \frac{ 1 + f(x)g(x) } + { \sqrt{1 - \sin x} } + \right) \, dx\\ + &= \int \frac{ 1 + f(x) } + { 1 + g(x) } \, dx - 2 \arctan (x - 2) + \end{aligned} +\end{equation} + +\[ + \begin{aligned}[b] + x &= 3 + \mathbf{p} + \alpha \\ + y &= 4 + \mathbf{q}\\ + z &= 5 + \mathbf{r} \\ + u &=6 + \mathbf{s} + \end{aligned} + \text{\qquad using\qquad} + \begin{gathered}[b] + \mathbf{p} = 5 + a + \alpha \\ + \mathbf{q} = 12 \\ + \mathbf{r} = 13 \\ + \mathbf{s} = 11 + d + \end{gathered} +\] + +% 5.6.2 Split + +\begin{equation}\label{E:mm7} + \begin{split} + (x_{1}x_{2}&x_{3}x_{4}x_{5}x_{6})^{2}\\ + &+ (x_{1}x_{2}x_{3}x_{4}x_{5} + + x_{1}x_{3}x_{4}x_{5}x_{6} + + x_{1}x_{2}x_{4}x_{5}x_{6} + + x_{1}x_{2}x_{3}x_{5}x_{6})^{2} + \end{split} +\end{equation} + +\begin{align}\label{E:mm8} + \begin{split} + f &= (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\ + &= (x_{1} x_{2} x_{3} x_{4} x_{5} + + x_{1} x_{3} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}, + \end{split}\\ + g &= y_{1} y_{2} y_{3}.\label{E:mm9} +\end{align} + +\begin{gather}\label{E:mm10} + \begin{split} + f &= (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\ + &= (x_{1} x_{2} x_{3} x_{4} x_{5} + + x_{1} x_{3} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{4} x_{5} x_{6} + + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}\\ + &= (x_{1} x_{2} x_{3} x_{4} + + x_{1} x_{2} x_{3} x_{5} + + x_{1} x_{2} x_{4} x_{5} + + x_{1} x_{3} x_{4} x_{5})^{2} + \end{split}\\ + \begin{align*} + g &= y_{1} y_{2} y_{3}\\ + h &= z_{1}^{2} z_{2}^{2} z_{3}^{2} z_{4}^{2} + \end{align*} +\end{gather} + +% 5.7 Adjusted columns + +\begin{equation*} + \left( + \begin{matrix} + a + b + c & uv & x - y & 27\\ + a + b & u + v & z & 1340 + \end{matrix} + \right) = + \left( + \begin{matrix} + 1 & 100 & 115 & 27\\ + 201 & 0 & 1 & 1340 + \end{matrix} + \right) +\end{equation*} + +\begin{equation*} + \left( + \begin{array}{cccr} + a + b + c & uv & x - y & 27\\ + a + b & u + v & z & 1340 + \end{array} + \right) = + \left( + \begin{array}{rrrr} + 1 & 100 & 115 & 27\\ + 201 & 0 & 1 & 1340 + \end{array} + \right) +\end{equation*} + +\begin{equation}\label{E:mm11} + f(x) = + \begin{cases} + -x^{2}, &\text{\CMR if $x < 0$;} \\ + \alpha + x, &\text{\CMR if $ 0 \leq x \leq 1$;}\\ + x^{2}, &\text{\CMR otherwise.} + \end{cases} +\end{equation} + +% 5.7.1 Matrices + +\begin{equation*} + \left( + \begin{matrix} + a + b + c & uv & x - y & 27 \\ + a + b & u + v & z & 1340 + \end{matrix} + \right) = + \left( + \begin{matrix} + 1 & 100 & 115 & 27 \\ + 201 & 0 & 1 & 1340 + \end{matrix} + \right) +\end{equation*} + +\begin{matrix} + a + b + c & uv & x - y & 27 \\ + a + b & u + v & z & 134 +\end{matrix} + +\begin{equation}\label{E:mm12} + \setcounter{MaxMatrixCols}{12} + \begin{matrix} + 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\\ + 1 & 2 & 3 & \hdotsfor{7} & 11 & 12 + \end{matrix} +\end{equation} + +\begin{equation}\label{E:mm12dupl} + \setcounter{MaxMatrixCols}{12} + \begin{matrix} + 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\\ + 1 & 2 & 3 & \hdotsfor[3]{7} & 11 & 12 + \end{matrix} +\end{equation} + +% Matrix variants + +\begin{alignat*}{3} + &\ + \begin{matrix} + a + b + c & uv\\ + a + b & c + d + \end{matrix} + \qquad + & & + \begin{pmatrix} + a + b + c & uv\\ + a + b & c + d + \end{pmatrix} + \qquad + & & + \begin{bmatrix} + a + b + c & uv\\ + a + b & c + d + \end{bmatrix} + \\ + & + \begin{vmatrix} + a + b + c & uv\\ + a + b & c + d + \end{vmatrix} + \qquad + & & + \begin{Vmatrix} + a + b + c & uv\\ + a + b & c + d + \end{Vmatrix} + \qquad + & & + \begin{Bmatrix} + a + b + c & uv\\ + a + b & c + d + \end{Bmatrix} +\end{alignat*} + +\begin{equation*} + \left( + \begin{matrix} + 1 & 0 & \dots & 0 \\ + 0 & 1 & \dots & 0 \\ + \vdots & \vdots & \ddots & \vdots\\ + 0 & 0 & \dots & 1 + \end{matrix} + \right] +\end{equation*} +\end{verbatim} +which produces +\begin{equation*} + \left( + \begin{matrix} + 1 & 0 & \dots & 0 \\ + 0 & 1 & \dots & 0 \\ + \vdots & \vdots & \ddots & \vdots\\ + 0 & 0 & \dots & 1 + \end{matrix} + \right] +\end{equation*} + +% Small matrix + +$\begin{pmatrix} + a + b + c & uv\\ + a + b & c + d +\end{pmatrix}$ + +$\left( +\begin{smallmatrix} + a + b + c & uv \\ + a + b & c + d +\end{smallmatrix} +\right)$ + +% 5.7.2 Arrays + +\begin{equation*} + \left( + \begin{array}{cccc} + a + b + c & uv & x - y & 27 \\ + a + b & u + v & z & 134 + \end{array} + \right) +\end{equation*} + +% 5.7.3 Cases + +\begin{equation} + f(x)= + \begin{cases} + -x^{2}, &\text{if $x < 0$;}\\ + \alpha + x, &\text{if $0 \leq x \leq 1$;}\\ + x^{2}, &\text{otherwise.} + \end{cases} +\end{equation} + +% 5.8 Commutative diagrams + +\[ + \begin{CD} + A @>>> B \\ + @VVV @VVV\\ + C @= D + \end{CD} +\] + +\[ + \begin{CD} + \mathbb{C} @>H_{1}>> \mathbb{C} @>H_{2}>> \mathbb{C} \\ + @VP_{c,3}VV @VP_{\bar{c},3}VV @VVP_{-c,3}V \\ + \mathbb{C} @>H_{1}>> \mathbb{C} @>H_{2}>> \mathbb{C} + \end{CD} +\] + +\[ + \begin{CD} + A @>\log>> B @>>\text{bottom}> C + @= D @<<< E + @<<< F\\ + @V\text{one-one}VV @. @AA\text{onto}A @|\\ + X @= Y @>>> Z + @>>> U\\ + @A\beta AA @AA\gamma A @VVV @VVV\\ + D @>\alpha>> E @>>> H + @. I\\ + \end{CD} +\] + +% 5.9 Pagebreak + +{\allowdisplaybreaks +\begin{align}\label{E:mm13} + a &= b + c,\\ + d &= e + f,\\ + x &= y + z,\\ + u &= v + w. +\end{align} +}% end of \allowdisplaybreaks |